Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
372 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624283 | C2 | semidirect |
| 2. C32×#709 | C2 | semidirect |
| 3. C2×C5×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. #10623767 | C2 | semidirect |
| 5. #10623763 | C2 | semidirect |
| 6. #10623762 | C2 | semidirect |
| 7. #10623758 | C2 | semidirect |
| 22. C3×#709 | D3 | semidirect |
| 42. C2×C3⋊(C3⋊C8) | D5 | semidirect |
| 60. #709 | C3⋊D3 | semidirect |
| 91. C32×C5 | #135 | semidirect |
| 144. C3×C5 | #950 | semidirect |
| 156. C32 | #4050 | semidirect |
| 172. C5 | #64159 | semidirect |
| 180. C3 | #91311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624283 | 2 |
| C32×#709 | 2 |
| C2×C5×C3⋊(C3⋊C8) | 2 |
| #10623767 | 2 |
| #10623763 | 2 |
| #10623762 | 2 |
| #10623758 | 2 |
| #91311 | 3 |
| #64159 | 5 |